Spline deformation of locally optimal trajectories: Feasibility and upper bound on control inputs

Abstract

Abstract-Deformation of optimal trajectories has a great potential in various applications due to the ability of realtime recomputation of the overall trajectory when applying new boundary conditions. This paper presents a novel approach where optimal trajectories are created offline through numerical direct optimal control methods. Afterwards the trajectories are deformed online with a spline deformation approach, providing minimum acceleration deviation between optimal and deformed trajectories and considerably reducing the computational complexity of the algorithm during run time. A feasibility check based on upper bounds for the deformed trajectory, the controller tracking error and the resulting torque is provided. This guarantees correct task execution in the presence of bounded disturbances and unmodeled dynamics.

Dynamically Consistent Online Adaptation of Fast Motions for Robotic Manipulators

“…Still, it wasn't capable of keeping desired derivative profiles and providing boundary conditions higher than velocities. In [35] we derived infinitynorm boundaries for robot joint torques in the case of the cubic spline interpolation. These bounds have a closed-form solution but are quite conservative in presence of external disturbance.…”

“…In [35] we derived bounds for ∞ norm for cubic spline deformation. These estimates could be generalized for the preservation of the n-th desired derivative and for the case of disturbance due to contacts and parametric uncertainty.…”